Lower Eyelid (blepharoplasty?) complications. Which are the most common? (Photo)

You will likely benefit from either surgery (lower blepharoplasty with fat repositioning) or filler injection in the hollow area.  Each has its pros and cons. Both are very safe, if done conservatively and under experienced hands. Eyelid surgery is as safe as dental work, if these factors are considered.

Fillers if done correctly will NOT make the fat look larger. It will smooth out the cheek to eyelid area so that you won't notice the fat and should appear smooth and less dark. The filler is not put into the fat but into the tear trough below the fat. At some point you could do a fat repositioning blepharoplasty, but you would be best to wait until you have more prolapsed fat.

Transconjunctival blepharoplasty for fat bags vs fillers? If fillers were used you look like it would make the "bag" larger. A TC blepharoplasty will remove the excess which can be used to fill the tear trough. Most common complication is over resection of fat. 

Your issue is best managed with under eye fillers.  You will have a much better results without surgery for the next 10 years or so.  The filler will need to be topped off periodically and possibly adjusted but you will have a much better aesthetic result with this approach.  The truth is that properly done, fillers are better than surgery.  People do sometimes say that they would rather have surgery because they will "save money" by having surgery.  This is a false economy.  Regarding potential risks of eyelid surgery, I encourage you to down load by fee book on eyelid surgery from my website.  This document has a very through discussion of the risks of eyelid surgery.  If you decide to have lower eyelid, it should be a transconjunctival arcus marginalis release surgery that preserves the lower eyelid volume and uses it to fill in the top of the cheek.

One of the most common complications associated with lower blepharoplasty is the aggressive removal of fat and skin. This can result in a hollow appearance which immediately makes a person look older, and also often shouts "I've had plastic surgery"  To avoid this look, be sure to view many, many before and after images from any plastic surgeon you are considering. Cosmetic lower eyelid surgery has undergone a paradigm shift over the twenty years since I began my plastic surgery training, as has facial rejuvenation surgery as a whole. The trend has been to move away from highly invasive procedures that focus on skin and fat excision and pulling skin structures as tight as possible (which tends to make a patient look less youthful and more like a stereotypical ‘plastic surgery patient’), and towards procedures that accomplish not only soft tissue preservation but also soft tissue enhancement – in the form of structural fat grafting. A typical 1970-1980’s era lower blepharoplasty usually consisted of the surgical removal of large volumes of lower lid fat, pulling the lower lid skin very tight and anchoring the lid laterally in a manner that often distorts the natural anatomy of the lateral canthus (lateral corner of the eye). I suppose you could say that this matches a windswept, pulled tight facelift - but it is not in any way truly rejuvenating. Current, state-of-the-art lower blepharoplasty focuses on soft tissue preservation, including some or most of what appears to be ‘herniated fat’. A number of techniques have been described that restore ‘herniated lower lid fat’ to a more ideal anatomic position, although ideally such a procedure leaves the orbital septum intact as shortening of the septum by suture tightening or cauterization carries with it some risk of lower lid retraction.   The trend has been towards limiting fat reduction to primarily older patients with very prominent lower fat pads. In many cases, the appearance of lower lid fat pad fullness can be effectively corrected by a combination of structural fat grafting of adjacent hollow areas like the tear troughs and tightening the orbicularis oculi muscles to the lateral orbital rim – which effectively restrains the fat pads and improves lower lid contour. Lateral orbicularis oculi muscle suspension is a very powerful means for reversing lower lid aging changes, and for doing so in a manner that does not distort natural lower lid external appearance. Preserving lower lid fat as much as possible, and restoring fullness in adjacent hollow areas by means of fat grafting, is a truly rejuvenating approach to lower lid surgery. Preserving and adding fat serves to enhance the soft tissue support of the lower lid and helps to maintain an ideal and youthful lower lid position over time. The more support you provide for the lower lid, the less you have to rely on internal support measures such as canthopexy and canthoplasty, which are useful for very lax and for overly long lower lids, but which also may distort the natural anatomy of the lower lid and upper lid.